Chapter 4: Quadratic Equations

Example – 14. The sum of the reciprocals of Rehman’s ages (in years), 3 years ago and 5 years from now is 1/3. Find his present age.

Solution :- Let his present age be x 

His age 3 years ago = x – 3 and 5 years hence = x + 5

A/Q           1/(x – 3 ) + 1/(x + 5) = 1/3
Or, (x + 5 + x – 3)/(x – 3)(x + 5) = 1/3
Or,   (2x + 2)/(x2 – 3x +5x – 15) = 1/3
Or,                    x² + 2x – 15 = 6x + 6
Or,                            x² – 4x – 21 = 0
Or,                           (x + 3)(x – 7) = 0

Either, x + 3 = 0 Or, x – 7 = 0

Thus, x = 7 or – 3; but age cannot be negative.

Hence his age is 7 years.